Could you be
A GRIEVER from the movie/book series, The Maze Runner (if you want to read the books or are a massive fan of the author, James Dashner, you can go here).
WARNING: SPOILER ALERTS WILL FOLLOW.
Looking for an exit? You won't escape that easily,
It is very difficult to escape the Maze.
Overwhelmed with hexes, I'll make you shift uneasily,
Every night, the Maze shifts position with a periodic pattern every month (at least, that is what I remember from the book). Also, the word hex means to "cast a spell on; bewitch". The pattern spells out words like a secret code: FLOAT - CATCH - BLEED - DEATH - STIFF - PUSH (here).
So many questions, but so little time,
When the first girl, Teresa, wakes up in the Box, she carries a note reading: She is the last one. Ever. Then supplies stop coming... and time starts to run out. Also, the Maze closes at night, and your time might run out if you get trapped inside!
Too few suggestions, forbidden to climb.
It is all so puzzling! And you cannot climb the walls of the Maze. (Book: it stretches high and tall forever, I believe. Movie: vines do not reach the top.)
Perhaps you follow the old adage, to have one hand always on me.
Some of the ol' fellas that have remained in the Glade (and perhaps in the Maze; i.e., during the daytime) from the very beginning (and not the Greenbeans) have seen the grievers...
A foolish attempt, useless baggage, you can never trust what you see.
You only see grievers when it's dark, and boy, you don't know what to expect when you are in the Maze... but of course, people need to carry "baggage" in order to defend themselves, particularly the Runners. There are also the Keepers, for which a guy by the name of Minho is the Keeper of the Runners... but there is also mention of a Keeper of the Baggers (here).
Take heed to be well prepared, or else I'll kill you when we meet.
That's what grievers are famous for (especially the taunting nightmares accompanied with their sting, ouch!). Thank God in the book, there is an antidote. (Not too sure about the movie.)
Hear my warnings and be scared, constant change my dominant feat.
I guess that refers to the stinger!
What am I?
The Web of Puzzles
Grievers look like giant spiders, and spiders make webs!
You come to me in groups, with lust in your hearts,
In the book, when the exit has finally been found, they are ready and prepared; they are willing to do whatever it takes to defeat the grievers, especially the group of them guarding the button in the exit!
You must defeat my troops, using your various arts.
That includes weapons and combat.
Gather together at the local place, there you'll learn about my dangers,
That must refer to the Glade (or the Homestead, but I am going with the former option).
My troops are armed with sword, spear, axe, and mace. Can you defeat all my rangers?
Grievers have all these kinds of similar weapons; they are unpredictable and very mechanical.
The only thing you remember when you wake up in the Box is your name. I love how this riddle was made by Joe-You-Know, as he definitely knows his name :D